Amplifier with adjustable gaintemperature response



United States Patent ANIPLIFIER WITH ADJUSTABLE TEMPERATURE RESPONSEThomas A. Prugh, Silver Spring, Md., and 'Charles'W. Durieux, Boston,Mass., assignors to the United States of America as represented by theSecretary of the y Application July 12, 1957, selialNo. 611,678

3 Claims. (Cl. 330-23) (Granted under Title .35, US. Code (1952), sec.266) The invention described herein may bemanufactured and used by orfor the Government for governmental purposes without the payment to usof any royalty thereon.

Our invention relates to amplifiers in. general and more particularly tomeans and methods for choosing and adjusting theamplification-temperature response of an amplifier. Theamplification-temperature response of an amplifier is the relationbetween amplier amplification and temperature.

It would be highly desirable in many applications to be able. to chooseor adjust the amplification-temperature response of an amplifier. "Forexample, the amplificationtemperature response of an amplifier may bechosen to,

compensate for the undesirable temperature response of a previous stage,may be chosen to prepare a signal for application to a stage having anundesirable temperature response or, if so desired, may "be chosen toprovide an amplifier having very good amplification stability over awide temperature range.

An object of this invention is to provide means and methods foradjusting the amplification-temperature response of an amplifier.

Another object is to provide means and methods for adapting a transistoramplifier to provide an amplification which remains substantiallyconstant with changes in temperature.

A further object is to provide a single-stage, singletransistoramplifier whose temperature response can 'be adjusted to provide anamplification-temperature response which rises at a predetermined rate,falls at a predetermined rate, and also can be adjusted to provide anamplification-temperature response which remains substantially constantwith changes in temperature.

Still another object is to provide a single-stage, singletransistoramplifier having an amplification-temperature response such that thereciprocal of the current amplification of the amplifier has a constanttemperature coeflicient which can be adjusted to have a predeterminedvalue.

Yet another object of this invention is to .provide an amplifier whosetemperature response can be adjusted to provide a predeterminedamplification-temperature response.

An additional object is to provide a method for adjusting thetemperature response of an amplifier to provide a predeterminedamplification-temperature response.

Another object of this invention is to provide an amplifier whoseamplification-temperature response has a minimum value at apredetermined temperature.

Yet another object is to provide a highv amplification transistoramplifier having an amplification which remains substantially constantwith changes in temperature. 1

In our invention the amplification-temperature response of an amplifieris adjusted by adjusting. the proportion of the input current applied tothe input of the amplifier. Byproper choice of this proportion and theassociated circuitry we have "been able to adapt an' amplifiertoproicevide a predetermined amplification-temperatureresponse.- The specificnature of the invention as well as other objects, uses and advantagesthereof will clearly appearl from the following description and from theaccompanying drawing, in which:

Figure 1 is a schematic diagram of a basic transistor amplifierequivalent circuit having an adjustable condu'ct ance g connected acrossits input.

Figure 2 is a circuit diagram of a single-stage common emittertransistor amplifier having the equivalent circuit of Figure 1.

Figure '3 is a theoretical plot of the temperature coefiicient m vs theinput conductance g, for a 2N77fty'pev transistor connected in thecircuit of Figure 1.

Figure 4 is a theoretical plot of vert I for several values of the inputconductance g using a 2N77 type transistor connected in the circuit ofFigure 2.1

"Figure 5 is a schematic diagram of four stages of Figure 2 cascaded.

Figure 6 is a theoreticalplot of for the cascaded stages of Figure '5.

Figure 1 shows a basic transistor amplifier equivalent circuit having anadjustable conductanceg connected across its input. This equivalentcircuit considers only low frequency (resistive) components and allcoupling and bypass capacitors are assumed to :have zero reactance. I V

The transistor T in Figure 1 is connected either come mon base, commonemitter, or common collector. "The conductance g represents thetransistor input conductance and the'symbol it represents the transistorcurrent amplification for the particular connection of'the transistor T.In Figure 1 a is the amplification withg; absent, that is g =0. Theadjustable conductance g represents the entire external circuitconductance to the left of the transistor T and is assumed to remainconstant with changes in temperature.

We will now show how the value of the conductance g can 'be adjusted toadjust the amplification-temperature response of the basic amplifierequivalent circuit of The current amplification A, may be writtenFigure 1. as follows:

For most transistors g varies with changes in temperature in alltransistor connections.

by controlling the ratio g /g made small so that g /g is small withrespect to 1, changes in g with temperature will causepractically nochange in A,. If g were zero, that is g were.

absent, the amplification-temperature response would depend only uponthe temperature variations in a.

It becomes evident therefore that the amplification-term.

' with a resistor in series with g rather than in parallel Anexamination-of the Equation 1 A, reveals that the effect on the currentgain. A, of variations in g with temperature may be adjusted Forexample, if g, is-

as shown by g The important feature is to provide for the adjustment ofthe proportion of the input signal which is applied to the amplifier.

For most transistors the transistor current amplification fa. and thetransistor input conductance g -fall or rise inopposite directions andthus have opposite etfects on the current amplification A It is possibletherefore, by proper choice of the ratio g g to adjust a transistoramplifier so that the eifeots of either a or g on the amplifier currentamplification predominate. For example, if in a particular amplifier ghas a negative temperature coeificient and a has a positive temperaturecoetficient, a choice of g will provide a risingamplification-temperature response for the amplifier. On the other hand,a choice of g /g much greater than 1 will provide a fallingamplification-temperature response if the temperature changes inpredominate over changes in a. Furthermore, it beis the parallelcombination of the adjustable resistor 10 and the source resistance 34;the conductance g represents the input conductance looking into thetransistor T into which the current i flows; and the symbol a 5represents the current gain of the transistor T taking into account theeffect of the emitter resistor R To illustrate how a predeterminedtemperature response may be provided for a transistor amplifier merelyby knowing the characteristics of certain transistor parameters, atheoretical expression for the amplification-temperature response of theillustrative single-stage amplifier of Figure 2 will now be derived. Asimilar derivation can be carried out for other types of transistoramplifier stages such as common collector or common base 16 stages.

It will be assumed that the transistor in Figure 2 operates into aresistance which is much less than the output impedance of thetransistor. This assumption is justified because a transistor amplifierordinarily operates into a low impedance. For example, if the transistoramplifier comes apparent that a value of g /g could be chosen in such anamplifier so that the temperature variations in .a and g will combine toprovide an amplificationt emperature response which remainssubstantially constant with variations in temperature. I

The above analysis may also be used for a transistor having a resistorin the common lead. In such a situation the values of g and a are merelychanged to include the efiects of this resistor. The preceding analysisvwill then apply.

The'above analysis may further be extended to adjust the amplificationtemperature response of any amplifier whose input conductance varieswith temperature and whose output current is dependent upon the inputcurrent to the amplifier. The symbol a will then represent the currentamplification of the amplifier with the conductance g omitted, that is gis equal to zero.

The preceding discussion shows how the amplificationtemperature responseof an amplifier may be adjusted when the variations in g and a withtemperature are known for a particular circuit. We will now show how theabove analysis can be applied to one type of transistor amplifier sothat a predetermined amplification-temperature response can be providedmerely by knowing the characteristics of certain transistor parameterscommonly supplied by the manufacturer.

Figure 2 shows the circuit to which the above analysis is applied. Asimilar application can be made for other types of transistor amplifiercircuits.

In Figure 2, the circuit between the dotted lines is a typicalsingle-stage common emitter transistor amplifier having an inputterminal and an output terminal 40. A resistor 26 represents the loadresistance of any circuit connected to the output terminal 40 and aresistor 34 represents the source resistance of a current source iflowing to the input terminal 30. The capacitor 22 serves as a D.-C.blocking capacitor.

The transistor T has its emitter 15, base 13, and collector 11 elementsconnected for common emitter operation. Negative current from a voltagesupply V is applied to the collector 11 through a collector resistor 24.The emitter 15 is biased by positive current flowing from a positivevoltage supply +V through an emitter bias resistor 14 and an emitterresistor R A bypass capacitor 12 is connected across the emitter biasresistor 14. The emitter resistor R is included to provide degenerationif so desired. The adjustable resistor 10 connected between the base 13and circuit ground is used to adjust the amplification-temperatureresponse of the amplifier. A capacitor 19 in the input circuit serves asa coupling capacitor.

The circuit of Figure 2 is one of many which may be represented bytheequivalent circuit of Figure 1. For the circuit of Figure 2 theadjustable conductance g operates into another similar transistor stage,the input resistance of that stage by itself is ordinarily sufficientlysmall to support the assumption. For applications where the amplifierfeeds a high impedance, the applicability of 26 this assumption can bemaintained by paralleling the Where h =current generated at the outputof the transistor T in the common base connection due to a unit currentat the input (a ratio) and h,-=input impedance of the transistor T inthe common base connection with the output short-circuited (ohms).

Equations 2 and 3 are derived using a method based on the indefiniteadmittance matrix discussed by I. Shekel in Matrix Representation ofTransistor Circuits, I.R.E. Proc., vol. 40, pp. 1493-1497, November1952. Equivalent forms of these equations have since been derived byothers in the art and their correctness has been verified byexperimentation. Substituting Equations 2 and 3 in Equation 1 gives:

Examination of Equation 4 shows three parameters which aifect thetransistor current amplification A These parameters are hf, h and(1+h,). For presently available alloy and grown junction triodetransistors, variations in hf from unit to unit or with temperature areextremely small. It can safely be assumed therefore that the numeratorof the amplifier current amplification equation A, remains constant withvariations in temperature. As regards the parameters h and (l+h;)however, experiments have shown that these parameters vary considerablywith temperature and in opposite directions. Furthermore, for presentlyavailable alloy and grown junction triode transistors, the variations ofthese parameters with temperature are approximately linear over a widetemperature range, that is they have constant temperature coefficients.

The fact that h, and (l-l-h have constant temperature coefficients isvery desirable and makes possible the use of linear expressions for thevariations in h and (1+h wi empe ature in-th eq a ion ior A. is. iportant to notehowever that this linearityin h and (1+h,) is dependentupon maintaining a. stable operating point which remains fixed withchanges in temperature. Those in the art will be able to choose the biasresistors 14 and 24 and the bias sources, V and +V to provide anoperating point which meets these requirements. Typical values .for thetemperature coefiicients of .a representa tive 2N77 type transistor atan operating point of 1 mi1li ampere emitter current are about 0.15 ohmper degree centigrade for h and about -.0Ol2 unit per degree centigradefor (l+h At 25 degrees centigrade the parameter h E45 ohms and theparameter Assuming a stable operating p'oint, the variations of h; and(l+h,) with changes in temperature may be expressed by the followinglinearrelationships:

i= i 1( 'd) and ;)o z( o) where t=temperature t ==reference temperatureh =value of I1 at t ('1+h,) =value of (1+h,) at t K =absolute value ofthe temperature coefficient of h in units of h per degree temperature K=absolute value of the temperature coefficient of (1-+h,) in units of(1+h,) per degree temperature Substituting the above relationships inEquation 4 and rearranging results in the following expression for thecurrent amplification A; of the transistor amplifierof Figure 1:

perature coefi-lcient. The equation for this slope may be written as:

A =value of A,- at -t 1( i e) !)0 where m1=percent change in per degreecentigrade change in temperature from t mt=temperature coefiicient ofthe amplifier.

From Equation 7 it is evident that the reciprocal of the currentamplification can be adjusted to have a desired predetermined constanttemperature coeificient merely by knowing the values of h and (1+h,) andtheir temperature coefi'icients K and K By using a potentiometer for theinput resistor 10 or the emitter resistor R or both, the constanttempera- *6 t m nt f he amplifie sane e adiue ed over a wide rangemerely by turning a knob.

We will now illustrate how the Equations 6 andJcan be applied to anactual transistor. 7 Figure 3 shows a theoretical curve of thetemperature coefiicient m vs. the conductance g for a 2N77 :typetransistor connected in the circuit of Figure 2. This curve iscalculated using Equation 7 with the emitter resistor R set equal tozero. For present purposes R is set equal to zero, but for applicationswhere degeneration is desired, R may be chosen accordingly. ,Thefollowing approximate values of k hf, (1+h,) K and K3 are applicable toa typical 2N77 type transistor operated at 1 milliampere emittercurrent.

h =45 ohms K =0.15 ohm per degree-centigrade K =().000 12 unit perdegree centigrade Figure 4 is a theoretical plot of Equation 6 forseveral values of the conductance g using a 2N77 type transistorconnected in the circuit of Figure 2. R is set equal to zero. Asindicated by Equation 6 the curve of A0 I VS- t is a straight linehaving the slope The value of g corresponding to the slope of each lineis obtained from Figure 3.

Figures 3 and 4 are calculated for a single stage transistor amplifier.By cascading a number'of stages an even greater variety ofamplification-temperature responses can be obtained. For example, Figure5 shows four stages cascaded, each of the stages being constructed asshown between thedotted lines in Figure 2. Assum ing a 2N77 typetransistor operated at 1 milliampere emitter current, the values of Rand g ofeach stage are chosen to provide a slope of mJ =O*.7O percentfor stage A and a slope of m =0.2 percent for each of the A stages usingthe derived expression for m. The resistor 34 represents the sourceresistance of the input current i and the resistor 26 represents a loadresistance. A capacitor 22 is used to block DC. from the load resistor26. The resistor .26 is chosen to be sulficiently small sothat stage Asatisfies the basic assumption that its load resistance is much smallerthan its output resistance. For the other three stages, the combinationof g and the input resistance of each subsequent. stage is sufficientlysmall to satisfy this assumption. The conductance g of the first stageis made up of the parallel combination of the resistor 10 of the stage Aand the sourceresistance 34. The conductance g of the last three stagesis made up of the parallel combination of the resistor 10 of each stageand .the output resistance of the preceding stage. For practicalpurposes this output resistance is comprised essentially of thecollector resistor 24 since the output resistance of the 2N77 typetransistor will ordinarily be large in comparison.

Figure 6 shows the theoretical curves of i? vs. t

for the cascaded stages of Figure 5. Curve B is the reponse of stage Acurve C is the response of the three A, stages obtained by multiplyingtogether the responses of each individual A stage, and curve BC is theoverall response of the four stages obtained by multiplying togetherline B by curve C. I

' From'Figure 6 it becomes evident that an infinite variety ofpredetermined amplification-temperature responses can be obtained by theproper cascading of the amplifier stages of Figure 2. By using apotentiometer for R or g or both in one or more stages, a singleamplifier may be used to provide a Wide range of predeterminedamplification temperature responses. Those skilled in the art willunderstand how to choose the values of m for each amplifier stage ofFigure 5 so that maximum value of the curve BC occurs at almost anydesired temperature. Also, if it were desired that the curve BC have avalue rather than a maximum value, such a minimum value could beobtained by using the four-stage transistor amplifier of Figure 5 as afeedback amplifier. Furthermore, if so desired, considerably greatervariations in the shape of the amplification-temperature response curvecould be obtained by cascading more stages or by using'transistors whoseparameters vary at a greater rate than those of the 2N77 type transistorwhich was used for illustrative purposes in Figure -5. Still further,even greater versatility is possible by using appropriate thermistorelements in combination 'with the amplifier stages. For example athermistor element could be used for the resistor R or the resistor '10in Figure 2. p

A particularly desirable'and very important applicaiton of our inventionhas been to provide a high amplification transistor amplifier havingvery good amplification stability over a wide temperature range. Theprior art has had considerable difiiculty in providing such a stableamplifier. An examination of the equations for and m reveal that theamplification of the transistor amplifier stage will remain constantwith variations in tem-' perature when:

- 2=91 1 By cascading a number of stages, each of which satisfy Equation8, it is possible to produce a high amplification amplifier havingexceptionally good amplification stability over a wide temperaturerange. A specific transistor four-stage amplifier whose stagesapproximately satisfied Equation 8 was built and tested using stockitems. Tests showed that variations in temperature from 50 C. to +75 C.caused the amplifier amplification to vary less than ildb out of a totalamplification of 80db at 25 C. This compares with a 15db variation overthe same temperature range for an uncompensated transistor amplifier. Bya more careful choice of transistors and component values, even thisamplification stability can be improved.

It should be noted that the amplifier current amplification has beenused for the derviation of the equations presented. A similar but morecumbersome analysis is possible using amplifier voltage amplification.The use of either one or the other will not be of any real importancesince the amplification-temperature responses and the stageamplification will be the same no matter which one is used. It may alsobe noted that the actual value of the amplification was not considered.This also should cause no'difiiculty since those in the art will readilybe I 8 V V ableto provide any overall amplifier amplification by properchoice of g, or R for each stage, by the use of a particular number ofstages, or by using additional amplifiers.

It will be apparent that the embodiments shown are only exemplary andthat various modifications can be made in construction and arrangementwithin the scope of the invention as defined in the appended claims.

We claim:

1. A single-stage, single-transistor, common emitter amplifier having anamplification which remains substantially constant with changes intemperature, said amplifier comprising: a transistor having emitter,base and collector elements connected for common emitter operation, saidtransistor having values of h, and (1|h,) which have substantiallyconstant temperature coeflicients for a fixed operating point, thetemperature coeflicient of h, being positive and the temperaturecoefiicient (1+h',) being negative, h, being the input resistance ofsaid transistor in the common base connection with the outputshort-circuited, and It; being the current generated at the output ofsaid resistor in the common base connection due to a unit current at theinput, means for biasing said transistor, said means maintaining a fixedoperating point with changes in temperature, a load resistance connectedin the collector circuit of said transistor, said load resistance havinga value which is much less than the output resistance of saidtransistor, a resistance having a conductance g connected eifectivelyacross the emitter and base elements of said transistor, the value ofthe conductance g being chosen in accordance with the followingequation:

wherein K and K are the absolute values of the respective temperaturecoefficients of h and (1+h;) in units of h, per degree temperature andunits of (1+h,) per degree temperature respectively.

2. The invention in accordance with claim 1 wherein there isadditionally provided a resistor in series with said emitter, the valueof said resistor being chosen to provide a predetermined amount ofdegeneration.

3. A high amplification transistor amplifier having an amplificationwhich remains substantially constant with variations in temperature,said amplifier comprising a plurality of cascaded stages, each stagebeing constructed in accordance with claim 1.

References Cited inthe file of this patent UNITED STATES PATENTS2,431,306 Chatterjea et a1. Nov. 25, 1947 2,572,108 Chalhoub Oct. 23,1951 2,680,160 Yaeger June 1, 1954 2,773,945 Theriault Dec. 11, 19562,808,471 Poucel et a1. Oct. 1, 1954 2,833,870 Wilhelmsen May 6, 19582,848,564 Keonjian Aug. 19, 1958 OTHER REFERENCES Shea: Principle ofTransistor Circuits, Sept. 15, 1953, pages 164, 165, 177-179.

